Introduction to Credit Derivatives Uwe Fabich

Credit Derivatives 2 Outline  Market Overview  Mechanics of Credit Default Swap  Standard Credit Models

Credit Derivatives 3 Credit Derivatives Market Overview  Total Market Size > $5,000 billion  Growth rate of more than 30% over the last years  New Basel Capital Accord

Credit Derivatives 4 Credit Derivatives Market Overview  Product overview

Credit Derivatives 5 Credit Default Swap (CDS)  Most Basic Credit Derivatives Product  A CDS is used to transfer credit risk  Starting Point for pricing of Exotic Credit Derivatives  Investor can buy protection vs default of a reference entity- this is economically equivalent to shorting a credit

Credit Derivatives 6 Mechanics of a CDS  Premium leg: Protection buyer pays a spread at each date  Protection leg: Protection seller pays Face Value in exchange for bond if default occurs

Credit Derivatives 7 Credit Models  Structural Model - based on Merton (1974)  Reduced Form Model - based on Jarrow/Turnbull (1995)

Credit Derivatives 8 Merton Model  Lognormal stochastic process represents the firm‘s total Asset Value value  Default only occurs at maturity  Standard Black Scholes assumption  Shareholders are long a European Call on the firm‘s asset, Strike= Face Value of Debt  From Put-Call Parity: Debt= Risk Free Bond – European Put

Credit Derivatives 9 Merton Model  asset value and volatility are not observable  However, equity value and volatilty are. Black Scholes gives us: where  With these results we can price risky debt: where

Credit Derivatives 10  Once we have the value of the risky bond it is easy to calculate the credit spread:...and build a spread curve Example: (K=100; AV=140,115,98) Merton Model

Credit Derivatives 11 Problems with the Merton Model  Black Scholes assumptions do not hold  Only one zero coupon bond outstanding  Diffusion Model is continous  Pricing of Credit Derivatives with more exotic payoffs is beyond the limit of the model

Credit Derivatives 12 Reduced Form Model  Purpose: Arbitrage free valuation of default linked payoffs  Default is treated as exogenous event  Default event is the first event of a Poisson counting process.  Conditional probability of default is defined as hazard rate:...integration leads to the survival probality:

Credit Derivatives 13  Pricing of contingent claims if payment is made at time T: where if payment is made when default occurs: Probability of defaulting in time interval from t to t+dt is...and by integrating over the density of default time Reduced Form Model

Credit Derivatives 14 Reduced Form Model  Pricing CDS Spreads Present Value Protection leg Present Value Premium leg

Credit Derivatives 15 Reduced Form Model  Pricing CDS Spreads Protection Leg=Premium Leg

Credit Derivatives 16 Recovery Rates

Credit Derivatives 17 Conclusion There is a lot to learn for me But the rewards are high